Before I proceed with a resolution I would like to first confirm the timesheet template your users are using. You can check the template by going to Time sheet Templates and checking for the format type of the template assigned to your users.

Our custom timesheet format has the option to auto populate the next timesheet with the time data including the activity selection. On our custom timesheet format we have the following field:

John you can check the timesheet template as follows:

Go to AdministrationClick on UsersGo to the user profile and shift to Timesheet optionCheck the timesheet template assignedGo back to administrationClick on Timesheet template under timesheets sectionOpen the timesheet template assigned to the userCheck the Timesheet format